Surface cyclic quotient singularities and Hirzebruch–Jung resolutions
نویسنده
چکیده
If V is an affine algebraic variety and G ⊂ AutV a finite group of automorphism of V , the quotient variety is an affine algebraic variety V/G with a quotient morphism V → X = V/G. A point of X is an orbit of G on V , and the coordinate ring k[X] is the ring of invariants k[V ] of the induced action of G on k[V ]. This chapter studies the simplest case of this construction, when V = C and G = Z/r is the cyclic group of order r acting on C by diagonal matrixes; by a slight normalisation, we can assume that
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